A simple and versatile probabilistic reasoning scheme is presented. Based on an augmentation of a multi-dimensional inference space indexed by a Cartesian product of the fact and proposition sets, the scheme simplifies the processes involved in the representation and computation of a probabilistic reasoning system. In the augmented space, a set of auxiliary fields is utilized in addition to the fact-proposition relations to manipulate the uncertainty and incompleteness of the information presented. The scheme enhances the functionality of a probabilistic reasoning and facilitates the building of practical reasoning systems. The utilization of the augmented space in reasoning is illustrated by two problems in computer-vision applications.